We prove that if T is an R-tree with a minimal free isometric action of FN , then the Out(FN )-stabilizer of the projective class [T ] is virtually cyclic. For the special case where T = T+(φ) is the forward limit tree of an atoroidal iwip element φ ∈ Out(FN ) this is a consequence of the results of Bestvina, Feighn and Handel [6], via very different methods. We also derive a new proof of the T...

of D is an R-tree. (ii) There exists a tree (V, E ) whose vertex set V contains X, and an edge weighting C : E -i R that assigns a positive length C(e) to each edge e in E , such that D is the restriction of X to the shortest-path metric induced on V. (iii) There exists a map w : S(X) -i R>o from the set S(X) of all bi-partitions or splits of X into the set R ~ o of non-negative real numbers su...

‎Unmixed bipartite graphs have been characterized by Ravindra and‎ ‎Villarreal independently‎. ‎Our aim in this paper is to‎ ‎characterize unmixed $r$-partite graphs under a certain condition‎, ‎which is a generalization of Villarreal's theorem on bipartite‎ ‎graphs‎. ‎Also, we give some examples and counterexamples in relevance to this subject‎.

Existing encoding schemes and index structures proposed for XML query processing primarily target the containment relationship, specifically the parent–child and ancestor–descendant relationship. The presence of preceding-sibling and following-sibling location steps in the XPath specification, which is the de facto query language for XML, makes the horizontal navigation, besides the vertical na...

We propose a new algorithm to solve the problem of joining two spatial relations R and S when S is indexed by an R-tree. The method combines classical query processing techniques and a plane-sweeping algorithm. We compare our approach to the simple indexed-nested-loop method and to the state-of-the-art algorithms, and show through analysis and experiments on synthetic and real-life datasets tha...